Question

1. A soccer player kicks a soccer ball towards the goal. If she kicks it with a velocity of 24 m/s at an angle of 31 degrees above the ground, how high will the ball go?

Answer 1

To find the maximum height of a kicked soccer ball, the vertical component of the initial velocity is used with the equation for the maximum height in projectile motion. The height is calculated to be approximately 7.86 meters.

Step-by-step explanation:

The student is asking how high a soccer ball will go if it is kicked with a velocity of 24 m/s at an angle of 31 degrees above the ground. To determine the maximum height reached by the ball, one can use the vertical component of the initial velocity and the acceleration due to gravity. The vertical component of the velocity (Vy) is given by Vy = V * sin(θ), where V is the initial velocity and θ is the launch angle. The maximum height (H) can be found using the kinematic equation H = Vy2 / (2 * g), where g is the acceleration due to gravity (9.81 m/s2).

Applying the formula to the given values, Vy = 24 m/s * sin(31°) which calculates to approximately 12.43 m/s. Plugging this into the second formula gives H = (12.43 m/s)2 / (2 * 9.81 m/s2) which is approximately 7.86 meters. Therefore, the maximum height the ball will reach is about 7.86 meters above the ground.

Answer 2

The ball will go as high as 8.46 m

Step-by-step explanation:

Projectile Motion

It's the type of motion that experiences an object launched at a certain height above the ground and moves along a curved path exclusively under the action of gravity.

Being vo the initial speed of the object, θ the initial launch angle, and g the acceleration of gravity, then the maximum height hm can be calculated as follows:

`\displaystyle h_m=(v_o^2\cdot \sin^2\theta)/(2g)`

The soccer ball is kicked at a speed of vo=24 m/s at an angle of θ=31°. Taking the value of
`g=9.8 m/s^2`, then:

`\displaystyle h_m=(24^2\cdot \sin^2 31^\circ)/(2\cdot 9.8)`

`\displaystyle h_m=(576\cdot 0.2653)/(19.6)`

`h_m=7.80~m`

The ball will go as high as 8.46 m